Low order modelling of thermoacoustic instabilities and intermittency: Flame response delay and nonlinearity

Bonciolini, Giacomo; Faure-Beaulieu, Abel; Bourquard, Claire; Noiray, Nicolas

doi:10.1016/j.combustflame.2020.12.034

Cited by 34 publications

(24 citation statements)

References 49 publications

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“…17 in Ref. [90]). As shown in the latter reference, the linear growth rate ν and the nonlinear saturation κ can be adjusted to obtain a qualitative approximation of the experimentally measured phase space spanned by the acoustic pressure p and its time derivative ṗ.…”

Section: Theoretical Modelmentioning

confidence: 90%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker–Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

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Section: Theoretical Modelmentioning

confidence: 90%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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“…On the other hand, we illustrate how frequency-phase relationship could result in the observed behavior. In a sense, this follows the deduction on intermittency and other dynamical states [46,31], whereby properties of the observed intermittent behavior is elucidated by a stochastically forced Van-der-Pol oscillator in the former and the mean frequency locking in the latter.…”

Section: Dynamical States Derived From Experiments and Model Based Ap...mentioning

confidence: 70%

Understanding dynamical states observed in a thermo-acoustic system from perspective of frequency-phase relationship derived from a probabilistic oscillator model

Ramanan

Ramankutty

Sreed

et al. 2022

Preprint

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We perform lab scale experiments in a swirl combustor by reducing the equivalence ratio for two cases involving slightly different inlet air flow rates. Reduction in equivalence ratio at a constant air flow results in the combustor transiting from stable to unstable combustion. The transition passes through stable, type-2 intermittency and beat oscillations. The beat oscillations are seen to fluctuate at a single frequency, and hence suggestive of a process involving spatio-temporal variations in the phase of the driver (i.e., heat release rate fluctuations). This is understood in the manner of a reduced order model, where the driver is considered to an ensemble of phase oscillators with time delays and a probabilistic distribution of natural frequencies, similar to Kuramoto oscillator. The acoustic field is modeled as a Van-der-pol Duffing system, with natural frequency equal to the duct acoustic mode. The coupling between the oscillators is varied based on the physical premise of Rayleigh criterion. The coupled system is seen to qualitatively and quantitatively match the pressure data obtained from experiments. Insights into various conditions illustrate the role of mean and fluctuating instantaneous frequency amongst the phase oscillators in determining the modeled pressure oscillations. By quantifying the extent of fluctuating frequency coupling among the phase oscillators, it is observed that beat oscillations have high correlation with lower deviation compared to intermittency and stable oscillations.

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“…Low-order oscillator models of thermoacoustic instabilities have been validated in prior studies performed by our group [ 60 , 64 – 66 ], and are well understood in terms of their accuracy compared to higher-order models that include several eigenmodes, explicit time delay and non-antisymmetric nonlinear flame response to acoustic perturbations [ 67 ]. As is shown in fig.…”

Section: Set-upmentioning

confidence: 99%

Coupling-induced instability in a ring of thermoacoustic oscillators

Pedergnana

Noiray

2022

Proc. R. Soc. A.

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Thermoacoustic instabilities in can-annular combus-tors of stationary gas turbines lead to unstable Bloch modes which appear as rotating acoustic pressure waves along the turbine annulus. The multiscale, multiphysical nature of the full problem makes a detailed analysis challenging. In this work, we derive a low-order, coupled oscillators model of an idealized can-annular combustor. The unimodal projection of the Helmholtz equation for the can acoustics is combined with the Rayleigh conductivity, which describes the aeroacoustic coupling between neighbouring cans. Using a Bloch-wave ansatz, the resulting system is reduced to a single equation for the frequency spectrum. A linear stability analysis is then performed to study the perturbation of the spectrum by the can-to-can interaction. It is observed that the acoustic coupling can suppress or amplify thermoacoustic instabilities, raising the potential for instabilities in nominally stable systems.

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Low order modelling of thermoacoustic instabilities and intermittency: Flame response delay and nonlinearity

Cited by 34 publications

References 49 publications

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Understanding dynamical states observed in a thermo-acoustic system from perspective of frequency-phase relationship derived from a probabilistic oscillator model

Coupling-induced instability in a ring of thermoacoustic oscillators

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